Anyway after all the schematic shenanigans... back to the subject of a suitable PSU.

The PSU can be any DC type that is rated at 1A (or greater) with an output voltage of 15V DC to 17.5V DC. This would be for an unregulated type.
For a regulated type, the voltage range is slightly greater, 14.5V DC to 22V DC. A DC PSU is only a regulated type if it says it’s regulated on the label.

Of course, the polarity has to be correct unless you like magic smoke....

So are regulated the same as switching? If not are the methods of controlling voltage the same?

A good quality switching type (from now on I will use the acronym SMPSU for switch mode power supply unit) will most probably be regulated. These have a feedback system to sense the actual voltage at the output terminals. So that when the current required by the load (the device connected to it, like a computer) increases, or decreases, it can sense this and compensate. This ‘feedback’ is so quick that even with a multimeter on the output terminals, you should not see the voltage change. A good quality SMPSU if bought from a trusted load retailer (meaning in your own country) should also be safe and meet any requirements by the laws and regulations in your country.

Cheaper types of SMPSU are semi-regulated (for want of a better term). They don’t have the same level of ripple that an unregulated conventional (heavy because there is a 50Hz or 60Hz mains transformer inside) PSU suffers from. But the output voltage will drop as the current required by the load increases. This is because there is no sensing of the voltage at the output terminals. The control circuitry is all on the primary (mains) side.

Watch out for really cheap SMPSU. Especially those built to a price point. For example, for sale on eBay from China at low prices. Never mind that their performance is crap, the manufacturers think that the isolation gap between the mains side and the output side can be fractions of a mm wide ( 1/32 of an inch). Or that a single layer of thin tape is fine. And they mostly lack any radio interference components or any fuses.

In practice, if the cheaper design of SMPSU are safe (bought from a trusted load retailer), then for suppling a device which was originally powered by an unregulated conventional PSU, these units are fine.

Your TS2068 MIGHT have some bad capacitors. I also want to thank you very much for uploading the TS2068 technical book PDF file here yesterday or two days ago. Check these electrolytic capacitors numbers : c3 / c21 / c41 / c40 / c36/ c58 / c67 / c5 and c18. And a tantalum capacitor number is c71.

Having some experience with TS2068 I would also recommend a full recap of any electrolytic caps. With my TS2068 I was fighting with wash out colours and after recap they were back to NTSC normal. I would not worry about tantalum one as this type can last forever.

Tantalum types degrade in a different way. If a suitable voltage rated type has not been used, switch on cycles and voltage spikes will cause internal damage. Then they sometimes go short circuit. If the available supply current is high, they sometimes go BANG!

If however a suitable voltage rated type has been fitted, and the power on surge current is limited, then they can last a very long time.

Note that there are various criteria where the voltage rating should be derated. So typically in a circuit, their voltage rating should be triple the actual supply voltage. So on a 5V rail, use parts rated at 16V. For a 12V rail, use parts rated at 35V.

Don’t worry! I was a soldering noob before fitting my first ZX8-CCB and have progressed to being slightly less of a noob completely rebuilding a ZX81 (albeit rather slowly thanks to a duff 6.5 resonator) and having refurbished loads of Sinclairs. Rubber key Spectrums are good practice - plenty of caps.